Local effects of the quantum vacuum in Lorentz-violating electrodynamics

Abstract

The Casimir effect is one of the most remarkable consequences of the non-zero vacuum energy predicted by quantum field theory. In this paper we use a local approach to study the Lorentz violation effects of the minimal standard model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method similar to that used for obtaining the Born series for the scattering amplitudes in quantum mechanics, we compute, at leading order in the Lorentz-violating coefficients, the relevant Green's function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the stress-energy tensor in terms of the Green's function. We discuss its structure in the region between the plates. We compute the renormalized vacuum stress, which is obtained as the difference between the vacuum stress in the presence of the plates and that of the vacuum. The Casimir force is evaluated in an analytical fashion by two methods: by differentiating the renormalized global energy density and by computing the normal-normal component of the renormalized vacuum stress. We compute the local Casimir energy, which is found to diverge as approaching the plates, and we demonstrate that it does not contribute to the observable force.

arXiv comment15 pages, 1 figure

References in corpus (91)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Gravity at a Lifshitz Point
• Noncommutative Field Theory
• CPT Violation and the Standard Model
• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Data Tables for Lorentz and CPT Violation
• Gravity, Lorentz Violation, and the Standard Model
• Analogue Gravity
• Noncommutative Field Theory and Lorentz Violation
• Nonstandard optics from quantum spacetime
• Measurement of the Casimir force between parallel metallic surfaces
• Hopf Algebras, Renormalization and Noncommutative Geometry
• Testable scenario for Relativity with minimum-length
• Signals for Lorentz Violation in Electrodynamics
• Generalized Lorentz invariance with an invariant energy scale
• Stability, Causality, and Lorentz and CPT Violation
• Quantum gravity corrections to neutrino propagation
• Cosmological Constraints on Lorentz Violation in Electrodynamics
• The principle of relative locality
• Loop quantum gravity and light propagation
• One-Loop Renormalization of Lorentz-Violating Electrodynamics
• Repulsive Casimir Force in Chiral Metamaterials
• Stress Tensors and Casimir Energies in the AdS/CFT Correspondence
• Robust Limits on Lorentz Violation from Gamma-Ray Bursts
• Cross Sections and Lorentz Violation
• Vacuum Cherenkov radiation
• Causality and CPT violation from an Abelian Chern-Simons-like term
• Tunable Casimir repulsion with three dimensional topological insulators
• Low-energy Limits on the Antisymmetric Tensor Field Background on the Brane and on the Non-commutative Scale
• Bounding Noncommutative QCD
• The Cherenkov effect in Lorentz-violating vacua
• On the aether-like Lorentz-breaking actions
• Physical (ir)relevance of ambiguities to Lorentz and CPT violation in QED
• Comments on Non-Commutative Phenomenology
• Loop-Generated Bounds on Changes to the Graviton Dispersion Relation
• Constraints on Lorentz violation from gravitational Cherenkov radiation
• Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics
• Casimir Interactions for Anisotropic Magnetodielectric Metamaterials
• Covariant Horava-like and mimetic Horndeski gravity: cosmological solutions and perturbations
• Consistency of isotropic modified Maxwell theory: Microcausality and unitarity
• Improved Test of Lorentz Invariance in Electrodynamics
• Improved test of Lorentz Invariance in Electrodynamics using Rotating Cryogenic Sapphire Oscillators
• Addendum: Ultrahigh-energy cosmic-ray bounds on nonbirefringent modified-Maxwell theory
• Ultrahigh-energy cosmic-ray bounds on nonbirefringent modified-Maxwell theory
• Analysis of the consistency of parity-odd nonbirefringent modified Maxwell theory
• Repulsive Casimir effect from extra dimensions and Robin boundary conditions: from branes to pistons
• The Casimir Effect in the Presence of a Minimal Length
• Spacetime foam, CPT anomaly, and photon propagation
• Bare and Induced Lorentz and CPT Invariance Violations in QED
• Massive photons and Lorentz violation
• Casimir Effect in the Presence of Minimal Lengths
• Repulsive Casimir Effect with Chern insulators
• Covariant renormalizable gravity and its FRW cosmology
• The Casimir Effect in Minimal Length Theories based on a Generalized Uncertainity Principle
• Cerenkov Radiation in a Lorentz-Violating and Birefringent Vacuum
• One-Loop Renormalization of Pure Yang-Mills with Lorentz Violation
• Vacuum Cherenkov radiation in spacelike Maxwell-Chern-Simons theory
• Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators
• The Casimir Effect in the Presence of Compactified Universal Extra Dimensions
• The Energy Density in the Casimir Effect
• Gravitational Casimir effect
• One-Loop Renormalization of the Electroweak Sector with Lorentz Violation
• Classical Solutions in a Lorentz-violating Scenario of Maxwell-Chern-Simons-Proca Electrodynamics
• The Casimir Force in a Lorentz Violating Theory
• One-Loop Renormalization of QCD with Lorentz Violation
• Asymptotic states and renormalization in Lorentz-violating quantum field theory
• String Theoretic Bounds on Lorentz-Violating Warped Compactification
• Green's function approach to Chern-Simons extended electrodynamics: an effective theory describing topological insulators
• Classical Solutions in a Lorentz-violating Maxwell-Chern-Simons Electrodynamics
• Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics
• Casimir effect between ponderable media as modeled by the standard model extension
• Electro and magneto statics of topological insulators as modeled by planar, spherical and cylindrical $\theta$ boundaries: Green function approach
• A Green's function approach to the Casimir effect on topological insulators with planar symmetry
• Asymmetrically warped compactifications and gravitational Lorentz violation
• Electromagnetic description of three-dimensional time-reversal invariant ponderable topological insulators
• Quantum field theory based on birefringent modified Maxwell theory
• Generation of Axion-Like Couplings via Quantum Corrections in a Lorentz Violating Background
• Casimir-Polder intermolecular forces in minimal length theories
• Casimir Effect in Spacetime with Extra Dimensions -- From Kaluza-Klein to Randall-Sundrum Models
• Classical solutions for the Carroll-Field-Jackiw-Proca electrodynamics
• Stationary solutions for the parity-even sector of the CPT-even and Lorentz-covariance-violating term of the standard model extension
• Particle interference as a test of Lorentz-violating electrodynamics
• The full CPT-even photon sector of the Standard Model Extension at finite temperature
• Cherenkov Radiation with Massive, CPT-violating Photons
• Dynamical ambiguities in models with spontaneous Lorentz violation
• The Electromagnetic Field Stress Tensor between Dielectric Half-Spaces
• Diffraction in Time of Polymer Particles
• The Polymer Bouncer
• A Landscape in Boundary String Field Theory: New Class of Solutions with Massive State Condensation
• The Goldstone Theorem in non-linear electrodynamics

Cited by in corpus (27)

• Casimir effects in Lorentz-violating scalar field theory
• Maxwell electrodynamics modified by CPT-even and Lorentz-violating dimension-6 higher-derivative terms
• Gravitational waves effects in a Lorentz-violating scenario
• Maxwell electrodynamics modified by a CPT-odd dimension-five higher-derivative term
• Casimir effect in Lorentz-violating scalar field theory: a local approach
• Casimir effect of a Lorentz-violating scalar in magnetic field
• Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field
• Cold plasma waves in the chiral Maxwell-Carroll-Field-Jackiw electrodynamics
• Testing Lorentz- and CPT-invariance with ultracold neutrons
• New point-like sources and a conducting surface in Maxwell-Chern-Simons electrodynamics
• External sources in a minimal and nonminimal CPT-odd Lorentz violating Maxwell electrodynamics
• Casimir energy and topological mass for a massive scalar field with Lorentz violation
• Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation
• Interplay between chiral media and perfect electromagnetic conductor plates: repulsive vs. attractive Casimir force transitions
• Nonminimal planar electrodynamics modified by higher-derivative terms
• NLO radiative correction to the Casimir energy in Lorentz-violating scalar field theory
• Optical properties and energy propagation in a dielectric medium supporting magnetic current
• Anisotropic cold plasma modes in chiral vector Maxwell-Carroll-Field-Jackiw electrodynamics
• Material boundaries in Carroll-Field-Jackiw Lorentz-violating electrodynamics
• Constraining dimension-six nonminimal Lorentz-violating electron-nucleon interactions with EDM physics
• The Horava-Lifshitz Modifications of the Casimir effect at finite temperature revisted
• Optical reflection signature of an axion dielectric with magnetic current
• A dimension five Lorentz-violating nonminimal coupling for mesons in the KLZ model
• Casimir effect in polymer scalar field theory
• Constraining CPT-odd electromagnetic chiral parameters with pulsar timing
• Constraining EDM and MDM lepton dimension five interactions in the electroweak sector
• Scalar Casimir effect for a conducting cylinder in a Lorentz violating background